#line 1 "main.cpp" #define PROBLEM "https://yukicoder.me/problems/no/2602" #line 1 "/home/maspy/compro/library/my_template.hpp" #if defined(LOCAL) #include #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template vector argsort(const vector &A) { vector ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "/home/maspy/compro/library/other/io.hpp" #define FASTIO #include // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d: x) rd(d); } template void rd(vc &x) { for (auto &d: x) rd(d); } void read() {} template void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 4 "main.cpp" #line 2 "/home/maspy/compro/library/geo/base.hpp" template struct Point { T x, y; Point() : x(0), y(0) {} template Point(A x, B y) : x(x), y(y) {} template Point(pair p) : x(p.fi), y(p.se) {} Point operator+(Point p) const { return {x + p.x, y + p.y}; } Point operator-(Point p) const { return {x - p.x, y - p.y}; } bool operator==(Point p) const { return x == p.x && y == p.y; } bool operator!=(Point p) const { return x != p.x || y != p.y; } Point operator-() const { return {-x, -y}; } Point operator*(T t) const { return {x * t, y * t}; } Point operator/(T t) const { return {x / t, y / t}; } bool operator<(Point p) const { if (x != p.x) return x < p.x; return y < p.y; } T dot(Point other) { return x * other.x + y * other.y; } T det(Point other) { return x * other.y - y * other.x; } double norm() { return sqrtl(x * x + y * y); } double angle() { return atan2(y, x); } Point rotate(double theta) { static_assert(!is_integral::value); double c = cos(theta), s = sin(theta); return Point{c * x - s * y, s * x + c * y}; } }; #ifdef FASTIO template void rd(Point& p) { fastio::rd(p.x), fastio::rd(p.y); } template void wt(Point& p) { fastio::wt(p.x); fastio::wt(' '); fastio::wt(p.y); } #endif // A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1 template int ccw(Point A, Point B, Point C) { T x = (B - A).det(C - A); if (x > 0) return 1; if (x < 0) return -1; return 0; } template REAL dist(Point A, Point B) { A = A - B; T p = A.dot(A); return sqrt(REAL(p)); } // ax+by+c template struct Line { T a, b, c; Line(T a, T b, T c) : a(a), b(b), c(c) {} Line(Point A, Point B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; } Line(T x1, T y1, T x2, T y2) : Line(Point(x1, y1), Point(x2, y2)) {} template U eval(Point P) { return a * P.x + b * P.y + c; } template T eval(U x, U y) { return a * x + b * y + c; } // 同じ直線が同じ a,b,c で表現されるようにする void normalize() { static_assert(is_same_v || is_same_v); T g = gcd(gcd(abs(a), abs(b)), abs(c)); a /= g, b /= g, c /= g; if (b < 0) { a = -a, b = -b, c = -c; } if (b == 0 && a < 0) { a = -a, b = -b, c = -c; } } bool is_parallel(Line other) { return a * other.b - b * other.a == 0; } bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; } }; template struct Segment { Point A, B; Segment(Point A, Point B) : A(A), B(B) {} Segment(T x1, T y1, T x2, T y2) : Segment(Point(x1, y1), Point(x2, y2)) {} bool contain(Point C) { static_assert(is_integral::value); T det = (C - A).det(B - A); if (det != 0) return 0; return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0; } Line to_Line() { return Line(A, B); } }; template struct Circle { Point O; REAL r; Circle(Point O, REAL r) : O(O), r(r) {} Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {} template bool contain(Point p) { REAL dx = p.x - O.x, dy = p.y - O.y; return dx * dx + dy * dy <= r * r; } }; template struct Polygon { vc> points; T a; template Polygon(vc> pairs) { for (auto&& [a, b]: pairs) points.eb(Point(a, b)); build(); } Polygon(vc> points) : points(points) { build(); } int size() { return len(points); } template REAL area() { return a * 0.5; } template ::value, int> = 0> T area_2() { return a; } bool is_convex() { FOR(j, len(points)) { int i = (j == 0 ? len(points) - 1 : j - 1); int k = (j == len(points) - 1 ? 0 : j + 1); if ((points[j] - points[i]).det(points[k] - points[j]) < 0) return false; } return true; } private: void build() { a = 0; FOR(i, len(points)) { int j = (i + 1 == len(points) ? 0 : i + 1); a += points[i].det(points[j]); } if (a < 0) { a = -a; reverse(all(points)); } } }; #line 1 "/home/maspy/compro/library/geo/triangle_area.hpp" template REAL triangle_area(Point A, Point B, Point C) { return abs((B - A).det(C - A)) * 0.5; } #line 3 "/home/maspy/compro/library/geo/outcircle.hpp" template Circle outcircle(Point A, Point B, Point C) { REAL b1 = B.x - A.x, b2 = B.y - A.y; REAL c1 = C.x - A.x, c2 = C.y - A.y; REAL bb = (b1 * b1 + b2 * b2) / 2; REAL cc = (c1 * c1 + c2 * c2) / 2; REAL det = b1 * c2 - b2 * c1; REAL x = (bb * c2 - b2 * cc) / det; REAL y = (b1 * cc - bb * c1) / det; REAL r = sqrt(x * x + y * y); x += A.x, y += A.y; return Circle(x, y, r); } // ABC の外接円に対して内外どちらにあるか // 中:1, 境界:0, 外:-1 // 座標の 4 乗がオーバーフローしないようにする template int outcircle_side(Point A, Point B, Point C, Point p) { T d = (B - A).det(C - A); assert(d != 0); if (d < 0) swap(B, C); array, 3> pts = {A, B, C}; array, 3> mat; FOR(i, 3) { T dx = pts[i].x - p.x; T dy = pts[i].y - p.y; mat[i][0] = dx, mat[i][1] = dy, mat[i][2] = dx * dx + dy * dy; } T det = 0; det += mat[0][0] * mat[1][1] * mat[2][2]; det += mat[0][1] * mat[1][2] * mat[2][0]; det += mat[0][2] * mat[1][0] * mat[2][1]; det -= mat[0][0] * mat[1][2] * mat[2][1]; det -= mat[0][1] * mat[1][0] * mat[2][2]; det -= mat[0][2] * mat[1][1] * mat[2][0]; if (det == 0) return 0; return (det > 0 ? 1 : -1); } #line 7 "main.cpp" using P = Point; void solve() { LL(Q); P A, B, C; read(A, B, C); A.x *= 2; A.y *= 2; B.x *= 2; B.y *= 2; C.x *= 2; C.y *= 2; FOR(3) { tie(A, B, C) = mt(B, C, A); ll dot = (B - A).dot(C - A); if (dot < 0) { P O = (B + C); O.x /= 2, O.y /= 2; A = B - O; tie(A.x, A.y) = mp(A.y, -A.x); A = A + O; } } FOR(Q) { P p; read(p); p.x *= 2, p.y *= 2; Yes(outcircle_side(A, B, C, p) >= 0); } } signed main() { int T = 1; // INT(T); FOR(T) solve(); return 0; }